Advertisements
Advertisements
Question
The length of the diagonals of a rhombus is in ratio 4 : 3. If its area is 384 cm2, find its side.
Advertisements
Solution
Let the lengths of the diagonals of a rhombus are 4x, 3x.
∴ Area of the rhombus = `1/2 xx ("Product of its diagonals")`
= `1/2 (4x xx 3x) = 384` (given)
⇒ `6x^2 = 384 ⇒ x^2 = 64`
⇒ x = 8 cm
∴ Diagonals are `4 xx 8 = 32` cm and `3(8) = 24` cm.
∴ OC = 16 cm and OD = 12 cm
∴ Side DC = `sqrt("OC"^2 + "OD"^2)`
∴ Side DC = `sqrt(16^2 + 12^2)` [By Pythagoras Theorem in ΔDOC]
= `sqrt(256 + 144) = sqrt(400) = 20` cm
Hence , side of the rhombus = 20 cm.
APPEARS IN
RELATED QUESTIONS
Lengths of the diagonals of a rhombus are 16.5 cm and 14.2 cm, find its area.
Find the area of rhombus PQRS shown in the following figure.
Find the area of a rhombus whose base is 14 cm and height is 9 cm.
The area of a rhombus is 100 sq.cm and length of one of its diagonals is 8 cm. Find the length of the other diagonal
The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is ______.
If the diagonals of a rhombus get doubled, then the area of the rhombus becomes ______ its original area.
The area of a rectangular field is 48 m2 and one of its sides is 6 m. How long will a lady take to cross the field diagonally at the rate of 20 m/minute?
The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m, and 350 cm respectively. Find the cost of plastering at the rate of Rs 8 per m2.
Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area sail of the sailboats to the nearest tenth.
Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area of sail of the sailboats to the nearest tenth.
